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Primes of the form Sum_{k=1..s} (k*(k+1)/2)^r for some integers r > 0 and s > 1.
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%I #6 Jun 08 2021 02:35:03

%S 62003,380862171499238015813159,

%T 477178536605483099069547874229030876125647161030458264473574997121391,

%U 206419274016718024802773356759257053810224508067009725029122120681133886193

%N Primes of the form Sum_{k=1..s} (k*(k+1)/2)^r for some integers r > 0 and s > 1.

%C Terms are the primes that equal the sum of the r-th powers of the first s triangular numbers. For first 5 listed terms the corresponding pairs of integers r and s are {r,s} = { {4,5}, {12,13}, {26,29}, {27,33}, {90,5} }. There are also known terms corresponding to {r,s} = { {35,285}, {144,5}, {141,37}, {179,13} } which are too large to include.

%Y Cf. A019434 (Fermat primes: primes of the form 2^(2^k) + 1).

%K nonn

%O 1,1

%A _Alexander Adamchuk_, May 08 2007